It might be onion root maggots ... both the timing and the damage sound about right. If it is, you'll see white worms that are about 1/2 inch long in the stems.

I've never seen any bug or worm, but I know that the last crop had several onions in it with a tube like burrowing in them. It had to have been a maggot or worm, but to never see them seems so strange. Anyway, should I try Seven or something do you think?

First off, I'd make sure to rotate your crop placement since if they're maggots, they overwinter in the top few inches of the soil and then come out again in spring so things like floating row covers won't help for the first generation. Then I'd probably recondition the planting beds this summer so that any organics like manure have a chance to break down a bit. When you plant in spring, if your soil pH can take it, I'd add some wood ashes to the top of the soil as a deterrent or try a layer of sand on top of the soil which they don't like.

It's been a long time since I've used heavy insecticides but if you're trying to kill the maggots that are there now, I think something like whatever replaced diazanon (Triazicide?) might do it but check the label to be sure.

All the onions are gone now anyway, and I would rather not use any pesticide if I can avoid it. So I will try that stuff for next year and see what happens. Thanks for your advice.